PROVIDENCE, R.I. — Rhode Island may be poised to become the next state to legalize same-sex marriage as bills were introduced Thursday in the state’s House and Senate chambers aimed at doing just that.

The move comes just two days after Governor Lincoln Chafee, in his inaugural address, called on legislators to swiftly legalize same-sex marriage, so that Rhode Island could “catch up to her New England neighbors.’’

The two bills, reintroduced in the House by Rep. Arthur Handy, and in the Senate by Sen. Rhoda Perry, call for legalizing “civil marriage” between people of the same gender, while specifying that no religious institution would be required to marry same-sex couples if it goes against its teachings.

The House bill was co-signed by 29 lawmakers, including House Speaker Gordon D. Fox, who is openly gay. Senate President Teresa Paiva Weed (D) opposes gay marriage, but her spokesman said she won’t block a vote on the legislation.

Efforts to legalize gay marriage in Rhode Island have been introduced several times in recent years, but failed due to opposition from former Gov. Donald L. Carcieri, a Republican, and previous legislative leaders.